On Topologies Induced by Ideals, Primals, Filters and Grills.

In this paper, one-to-one correspondences and equivalences between ideals, primals, filters and grills are introduced. It is shown that the local functions and the topological spaces induced by them are the same. From this point of view, the topological properties of one topology can be derived from the topological properties that are valid in the corresponding topology. [ABSTRACT FROM AUTHOR]